Flying Distance

Consider 4 (dimensionless) flies. They are situated at the corners of a square whose side is 1 meter. Each fly tries to reach the another fly in front of it. Since the flies are flying towards another, they will meet each other at a certain time in the center of the square. The Question is what is the length of the path they have travelled at the moment they reach each other?

Answer:

Because all flies constantly fly perpendicular to another fly, they all travel the shortest distance to each other, which is 1 meter (all flies make a kind of spiral flight to the center of the square, and during this flight, the flies constantly form a square until theymeet in the center). Therefore the flies all travel 1 meter each.